A deceivingly difficult integral 

Oily-Macaroni

Interestingly enough, I've just read it in a french instagram post too ! What term do US/UK native speakers usually use to name it?

@@sanamite I guess they call it a "change of variable". It's interesting to me that the idiom exists in French. "King's property" sounds like royal real estate to me. :D

Wow there were alot in this video

@@maths_505 Yes, and you can notice that at 4:11 I spotted them both, the reason for this is that, at this time, you said something about my counting, unfortunately I don't understand what, but it ends with "thank you very much", or some thing like that, so I'm not that worried 😃. It's a pleasure for me. By the way could you make a video about the alternate ways(1) of prooving that zeta(2)=pi^2 / 6 . There is one that starts from int_0^infty { int_0^infty { dx dy / (1-xy) }} that is not that easy, because it involves a couple of variable substitutions a bit tricky. (1) otherwise than the famous Euler proof.

I remembered now, I solved by simplifying. Integral Term is: Int(0 - π/2) (x²/2) { tan(x/2) + tan(π/4 - x/2) }dx = Int(0 - π/2) (1/2) { x² + (π/2 - x)² } tan(x/2) dx Now it'll be easy, Substitute, (1/2)tan(x/2) = sinx - sin2x + sin3x - sin4x + ......... And booooom.

or I =int x ln （1+ tan au ） dx，using feymann trick, but it seems that I got an much simpler solution through this ode, I am not sure if I am right.dI/da=C-I*2/a

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-mqPTvELJPM0.html

(with musical effects) you've got a friend in me

@@maths_505 🤩

It honestly looks kinda innocent....throw in an x² and a couple trig functions....and then you question all your life decisions leading up to that point 💀